Formal methods initially focused on the mathematically precise speci cation, design and analysis of functional aspects of so ware and hardware systems. In this context, model checking has proved to be tremendously successful in analyzing qualitative properties of distributed systems.is observation has encouraged people in the eld of performance and dependability evaluation to extend existing model checking techniques to also account for quantitative measures. As a result, nowadays, the automatic analysis of Markovian models has become an indispensable tool for the design and evaluation of safety and performance critical systems.Markovian models are classi ed according to their underlying notion of time, being either discrete or continuous. In the discrete-time setting, Markov decision processes are a nondeterministic model which is widely known in mathematics, computer science and operations research. Moreover, e cient algorithms are available for their analysis.is stands in sharp contrast to the continuous-time setting, where no techniques exist to analyze models that combine stochastic timing and nondeterminism. In the present thesis, we bridge this gap and propose quanti ably precise model checking algorithms for a variety of nondeterministic and stochastic models.We rst consider continuous-time Markov decision processes (CTMDPs). To uniquely determine the quantitative properties of a CTMDP, all its nondeterministic choices must be resolved according to some strategy. erefore, we propose a hierarchy of scheduler classes and investigate their impact on the achievable performance and dependability measures. In this context, we identify late schedulers, which resolve the nondeterminism as neatly as possible. Apart from their interesting theoretical properties, they facilitate the analysis of locally uniform CTMDPs considerably. In a locally uniform CTMDP, the timing in a state is independent of the scheduler. is observation culminates in an e cient and quanti ably precise approximation algorithm for locally uniform CTMDPs.In contrast to CTMDPs which closely entangle nondeterminism and stochastic time, interactive Markov chains (IMCs) are a highly versatile model that strictly uncouples the two aspects. Due to this separation of concerns, IMCs are locally uniform by de nition.is allows us to apply analysis techniques which are similar to those that we developed for locally uniform CTMDPs, also to IMCs. In this way, we solve the open problem of model checking arbitrary IMCs.In the next step, we return to CTMDPs and prove that they can be transformed into alternating IMCs in a measure preserving way. As our proof does not rely on local uniformity, it enables the analysis of quantitative measures on arbitrary CTMDPs by model checking their induced IMCs. However, the underlying scheduler class slightly di ers viii from the late schedulers that we used initially. In fact, it coincides with the time-and history dependent schedulers that are proposed in the literature. us, our result for IMCs also solves the lon...
